### On the Two-Body Problem

 Figure 1: The two-body problem. Image taken from this blog

In academia there is something called the "two-body problem." The original two-body problem involves the gravitational interaction between two massive bodies, e.g. a planet orbiting a star. This is a problem in the mathematical sense, as in something interesting about the universe that we would like to figure out. This classical two-body problem has a solution, but interestingly it is in the form of a transcendental equation that can only be solved numerically. But when done so, it looks like this. Pretty nice, huh?

It turns out that there's an even more difficult two-body problem in science academia, but this one has to do with the attraction between two humans (cf Figure 1 above for a succinct description). The problem arises when one or both individuals are academics seeking post-graduate job positions. The problem, in a traditional sense of the word, is related to the fact that academia has been honed and perfected over the centuries to accommodate only a specific type of coupling. If you are an academic and in a relationship, there is a closed-form solution to the two-body problem if and only if the partner/spouse is not also an academic and has the ability/willingness to move every 2-3 years over the next six years while academic partner takes various postdocs and/or other job positions. Personally, I was fortunate to find this "solution." Most do not.

A further complication from the standpoint of young academic couples is that there is often only one or at most a few available/desirable job openings per institution per year. This means that it is highly unlikely that the coupled academics will find their ideal job position at the same institution. However, if they do solve the problem at the postdoc level, it is very unlikely that it'll happen again at the professor level. Think of multiplying two or more small probabilities; the result is a very small chance. On the other hand, if you have a traditional (read: 1950's-era) family, none of this is really a problem. One partner pursues their career, the other raises the family, and the solution is not only closed-form, but elegantly analytic.

However, in modern times there have arisen a whole host of complications. The primary one is that as more and more women enter graduate programs, more and more couplings are occurring within said grad programs---hot nerd-on-nerd action, if you will. In what follows, please allow me to apply a cold scientific analysis to an inherently human/emotional process (I'm already bracing myself or angry commenters noting that not all women date men in academia. Settle down nerds, I recognize and hereby acknowledge the difference between a simplifying assumption and reality, the difference between the mean and the dispersion of a distribution of human behavior.)

Since the male-female ratio in most grad astro programs is 2:1---which is very high among the sciences, but still far from parity---there will be more women with two-body problems than men, under the simplifying assumption that every woman couples to a man. For every 3 intradepartmental pairings, there are four men available (forced) onto online dating services, night clubs, etc. where they can meet a non-academic. As the male-female ratio increases, the frequency of two-body problems among women increases. This assumption is valid, in my opinion, given that astro grad students spend the majority of their waking hours in their offices doing problem sets, reading papers, and tracking down bugs in their data reduction and numerical integration codes, instead of hanging out where non-academic, single people congregate. And if one's soulmate is not in the same department, there's always Bio or Engineering across the street!

This hypothesis gives rise to a few predictions:

1. The majority of women in science will be in a relationship with another academic. Here's a test providing confirmation of this prediction.
2. The unequal male/female ratio will result in more women than men facing a two-body problem
3. Societal norms and/or other pressures will result in the woman giving up her career more frequently than the man giving up his. Anecdotally, but very obviously, I've noticed that the men in two-body situations tend to be 1-4 years older than their partner, which means they are more established when the tough decision-time comes. With a man in an established job further along in his career, it is often the woman who gives up rolling the dice on a future opportunity in favor of the sure-thing right now with her partner’s job offer.
4. There will be a higher attrition rate among women than among men in academia, causing the male-female ratio to increase from grad school, to postdoc, to professor.
5. The refusal of science programs to acknowledge and address this problem will exacerbate the gender disparity among their faculty.

Based on my personal observations during travels to various institutions, these predictions seem to hold up. The vast majority of my female friends/colleagues are in relationships with another academics, quite frequently with other astronomers. And far from being just a cute name given to a societal phenomenon, the two-body problem is a Problem with a capital P.

 Figure from Dual Career Academic Couples: What Universities Need to Know (PDF)
I can't imagine cutting my astronomy career short at this phase in my life, so I can only imagine how difficult it is for people to be forced to decide between their careers and their relationships. I've heard of women being told, "Your spouse has an excellent job opportunity here. Would it be so bad to give up your career?" I have to admit that I've entertained such thoughts in the past. But I find it doesn't work when I apply this reasoning to myself. When I think about my passion for astronomy, and how my research is what causes me to go to bed late and wake up early, there's just no way I could imagine giving up my career and still finding full satisfaction in life. I'm a trained slayer of hard problems, and I live to to drive big telescopes across the sky. I'm also passionate about undergraduate and grad education of the type that can only be implemented effectively as a professor. How could I just give that up? So, no, it's not at all an option to ask a coupled scientist to give up their careers.

When couples are able to hold onto their pursuits, long-distance relationships are very common, which puts strains not only on the individuals, but also on their science. Being away from one’s partner for extended periods of time leads to stress and anxiety, whcih negatively impacts day-to-day work. Excellent candidates pass up opportunities at top institutions (justifiably) to stay with their spouse. Top profs at leading institutions drop out at the peak of their games to find a solution to the two-body problem. Postdocs pass up fellowship offers to stay close to home. I really wish these weren't the choices that young scientists have to face. Our field would be much happier with a closed-form solution to the two-body problem.

As we in astronomy begin to embrace diversity as a key ingredient for excellence, we must find a robust solution to the two-body problem. To keep the conversation moving forward, here are some solutions I have heard suggested or come up with on my own:

1. Make postdoctoral fellowships last 4-5 years, rather than 2-3. The extra years relieve pressure and stress on couples to immediately begin searching for the next job and reduces the number of times a postdoc must move before (hopefully) settling into a more permanent professorship.
2. Restructure job searches to allow for two-body hires. I've heard it argued that this is undesirable because it would require sacrifices in "excellence" to hire a spouse that isn't as "excellent" as the primary hire. But what good is hiring an excellent individual when they will be looking for a more accommodating position from day-one after starting at your university? How much excellence can be traded for an unhappy, loosely-bound workforce? On the flip side, think about how much more loyal your employees will be if hired together. You better believe they'll work harder than anyone else in your dept, and be far less likely to be enticed by competive offers later (immunity to poaching is valuable, no?). Also, think of the message you send to your entire workforce when you demonstrate the value of family security in your workforce.
3. Coordinate among departments to make mixed-academic hires. One department might have to make a bit of a sacrifice along the (percieved) excellence dimension this time, but think of what can be gained the next time around when their top applicant is coupled to another academic. Astronomy is not the only field facing the problem.
4. Recognize the considerable uncertainty in judging excellence in the traditional sense. How many previously-identified excellent hires didn't attain tenure at your institution and other top universities in the past 20 years? If hiring committees can miss that badly in one direction, why not hire the person who is deemed an 8/10 on your scale in order to retain the 10/10 in your dept now, with the recognition that that 8.0 is really 8 +/- 1

What have I missed? Discuss!

Jason said…
I like your post — I was lucky enough to solve our 2-body problem "the hard way" by more-or-less independently getting an offer for both me and Julia in the same department, although in retrospect we now know that Julia was horribly overqualified for the position she got (she's since been promoted to where she should be).

One bureaucratic and ethical difficulty in solving the 2-body problem is that there is sometimes only so much a department or university can do to hire a "trailing" spouse (i.e. not the one the department has targeted for hire). Anti-discrimination policies often require all hirings to be preceded by a job ad posting, and a good-faith effort to find the best applicant for that position. This breaks the cycle of the "old boys' network" that prevents quality minority or female or outside applicants from even being able to apply for a job that a plugged-in applicant gets through his or her adviser's network of buddies.

But the flip side is that it may be bureaucratically impossible to hire a "trailing spouse" if there are a lot of better-qualified job seekers in their field that would apply for the job you'd like to offer them, which means that you lose out on the outstanding applicants that need to solve the 2-body problem.

The asymmetry of the problem is especially difficult to deal with. This study shows that while men and women today have similar expectations of egalitarian marriages, if that's not possible men are much more likely to expect their wife to stay at home with the kids than the women are willing to stay at home themselves.

Three solutions I've seen (all of them with big problems):

Trailing spouses often have to take jobs that they are overqualified for so that they ARE the best applicant for the position. This is hardly ideal, because it typically leads to the trailing spouse hoping and training for a research position but stuck with heavy teaching loads as a lecturer or adjunct professor on a semester-by-semester basis.

Another solution I've seen is to have two people share a position. That is, a single faculty "slot" is held by both spouses, who are paid as though they were one person (though benefits have to be a bit higher so they can both be covered) and have the committee and teaching loads of one faculty member. The department gets an extra member at little added cost, and the couple gets a light service and teaching load. This works best as a temporary solution while they look for a second "real" position. Also, they pay sucks.

Another common solution is for the trailing spouse to primarily target soft money, which they can use to get themself into an adjunct position at their partner's institution. The job security is terrible, but there are lots of people on soft money, and it's a workable solution. Of course, the trailing spouse has to be in a field that is amenable to a soft money career.

One possibility would be for Universities to explicitly create a way to hire spouses that are qualified, even if they are not the best qualified person they could get. This would be tricky to navigate against anti-discrimination policies and best practices, but if it is done in the interests of diversity and fairness it might work.
CosmicBabs said…
Hi John, Nice post. I've been in a long distance relationship for almost 4 years now. I don't image my life without astronomy but I'm quite unhappy with my actual situation. My partner tried to get a position near me here in the US but it did not happen (I graduated before him, he is an astronomer) and we are living in different continents. I'll be moving to Europe soon, I got a fellowship for 3(+2) years as a postdoc, basically for the reasons you give in your first solution point. I love what I do, and I'm happy I can go to a place where I can continue doing my research and where there is a "higher" chance that my partner could have a position too within the duration of the fellowship. It is still not ideal, he may not get a position in the same city/institution, but not moving for a couple of years sounds great, and give us more time to find opportunities to be together.
Maybe, there are "solutions" at the faculty level (like the ones Jason mentioned), but at the postdoc level things do not look very good. The postdocs without the 2-body problem I know were lucky to find open positions in the same city/institution, or one of the couple has quitted whatever he/she was doing before moving. The idea of quitting astro and the whole postdoc/permanent position hunt has crossed my mind more often than when I was in gradschool, by the fact that the issues related to the 2-body problem and gender do not seem to get better in the future job stages.
Elisabeth said…
The 2-body problem can also be an issue for graduate students. One thing I didn't realize going into the whole graduate school application process was that anybody cared. I think it's important for undergrads to know that it's something they should feel comfortable mentioning!
Interesting pie chart. I wonder what fraction of the 'single' pie are actually the result of "bound-free-transition" long distance two-body failures - I can tell you that's also a nontrivial population
Elena said…
Two thoughts:

1) Restructuring job searches can be done through cluster hires, where a 'cluster' of 3 or 4 TT positions are filled at once. These can be in the same department, but don't have to be. They can also revolve around a particular issue or area of study (e.g., "water", in which a limnologist, a sociologist, an atmospheric scientist, and a historian are hired). These types of hires can be additionally interesting for the university if they create real opportunities for collaboration across disciplines.

2) Another way Universities can help is by having some sort of spousal hire policy. For example, if a department is looking for a spousal hire, the University will pay 50% of the salary of the spouse until tenure *and* the spouse-hiring department doesn't lose whatever its next hire would have been. This makes the spouse a much more attractive hire to another department b/c they don't have to pay for someone who might not necessarily fit in their game plan for hiring over the next 5 years.

My two cents from someone who solved her two-body problem the hard way. (Two independent offers from two different universities in a big city.)
Amy P said…
Very interesting problem with a capital P. I see this happen in industry as well. Some companies do a good job of assisting spouses when the other is relocated. I know of assistance with paying for certification testing in new state, updated training for spouse in new state, etc. I know this 2-body problem has applied to friends who are both engineers, but I can definitely see how it's a bigger issue in academia. The pool of potential jobs and talent is considerably smaller, yes?
James Lloyd said…
There is a corollary to all of this from the perspective of a consumer in the job market: one of the most effective recruiting tools is the 2-body solution. Competition for the best grad students, postdocs and faculty can be fierce, and there are only so many things I can do to make my institution attractive to a potential recruit (especially with regards resources over which I have little control, e.g. access to 10m telescopes), and there's some pretty big Goliaths out there, especially in astronomy. As a practical matter, I have found effort expended on finding suitable solutions for a trailing spouse pays pretty good dividends. It's always challenging and I haven't always succeeded, but the effort is always appreciated and being willing to work hard on the 2-body problem can be an important competitive edge. Institutions that don't/can't address the 2-body problem are nuts because they are painting a great big bullseye in the middle of their forehead for David to aim at.
Excellent points, James! I've seen this from the Goliath side of things.
mq said…
There is a similar problem in the world of medicine when the medical students are applying to residency programs. The solution is what is known as couples match. In it, the couple is treated as an inseparable atomic unit. I don't know if they expose any of their algorithms (like, how the center of mass of the system is calculated), but since the process is a single, yearly, centralized optimization problem it is a little simpler than the multitude of independent postdoc and faculty hirings.

### On the Height of J.J. Barea

Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto).

Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship.

Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes.

So I decided to find a photo and settle the issue once and for all.

I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe…

### The Force is strong with this one...

Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1."

I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35."

Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out

x^2 - 1 = (x - 1) (x +1)

So $6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48$. That's actually pretty handy!

You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we…

### The Long Con

Hiding in Plain Sight

ESPN has a series of sports documentaries called 30 For 30. One of my favorites is called Broke which is about how professional athletes often make tens of millions of dollars in their careers yet retire with nothing. One of the major "leaks" turns out to be con artists, who lure athletes into elaborate real estate schemes or business ventures. This naturally raises the question: In a tightly-knit social structure that is a sports team, how can con artists operate so effectively and extensively? The answer is quite simple: very few people taken in by con artists ever tell anyone what happened. Thus, con artists can operate out in the open with little fear of consequences because they are shielded by the collective silence of their victims.
I can empathize with this. I've lost money in two different con schemes. One was when I was in college, and I received a phone call that I had won an all-expenses-paid trip to the Bahamas. All I needed to do was p…